Title: A sparse beta model with covariates for networks
Authors: Stefan Stein - University of Warwick (United Kingdom) [presenting]
Chenlei Leng - Warwick (United Kingdom)
Abstract: Data in the form of networks are increasingly encountered in modern science and humanity. We present a new generative model, suitable for sparse networks commonly observed in practice, to capture degree heterogeneity and homophily, two stylized features of a typical network. The former is achieved by differentially assigning parameters to individual nodes, while the latter is materialized by incorporating covariates. Similar models in the literature often include as many nodal parameters as the number of nodes, leading to over-parametrization. As a result, they can only model relatively dense networks. For estimation, we propose the use of the penalized likelihood method with an $\ell_1$ penalty on the nodal parameters, leading to a convex optimization formulation which immediately connects our estimation procedure to the LASSO literature. We highlight the differences of our approach to the LASSO method for logistic regression, emphasizing its feasibility to conduct inference for sparse networks, and study the finite-sample error bounds of the resulting estimator, as well as deriving a central limit theorem for the parameter associated with the covariates.